weil ein kurz Zeit danach, hatte er geheiratet.= because a short time after, he married.Don't try to copy English word order. The word "weil" signals the start of a subclause, so you must throw a switch in your mind and construct a subclause where the verb is at the end: weil er ... geheiratet hat. Now you fill in the rest: weil er eine kurze Zeit danach geheiratet hat.

"Darauf" is an adverb, but "after" is used as preposition in the English text: "after the discovery". As a preposition, "after" translates as "nach": Kurz nach der Entdeckung... When used as an adverb (e.g. "He discovered the dead mean shortly after"), "kurz darauf" is correct: Er entdeckte den toten Mann kurz darauf/danach. As a rule of thumb, the prefix "da-" signals that some prepositional (unmentioned) object has been turned into an adverb: nach X -> danach, für X -> dafür, auf X -> darauf, etc.

Hoffentlich, ein Licht werde

Again the "English comma": Whenever you catch yourself putting a comma in this place, it's probably wrong, and pay attention to word order.

I can only repeat myself: The German grammar patterns are different from the English ones. If you can't emulate them unconsciously, you must learn them consciously. Pick some German text (e.g. a Wikipedia article, or whatever), go over it in detail, maybe translate some part into English, and pay attention to where the patterns differ. Pay especial close attention to the placement of the verb. Maybe translate your English translation back after a day or two (so you can't remember the original text) and see if you arrive at the same word order.